Register Backend Module with Icon from FontAwesome (Tested with 8 LTS)

ext_localconf.php

<?php

if (!defined('TYPO3_MODE')) {
    die('Access denied.');
}

(function () {
    $iconRegistry = \TYPO3\CMS\Core\Utility\GeneralUtility::makeInstance(\TYPO3\CMS\Core\Imaging\IconRegistry::class);
    // Icons from: https://fontawesome.com/v3.2.1/icons/
    foreach (['shopping-cart', 'search'] as $icon) {
        $iconRegistry->registerIcon(
            'vendor-' . $icon,
            \TYPO3\CMS\Core\Imaging\IconProvider\FontawesomeIconProvider::class,
            [
                'name' => $icon,
            ]
        );
    }
})();

ext_tables.php

<?php

if (!defined('TYPO3_MODE')) {
    die('Access denied.');
}

(function () {
    /**
     * ######################################################################
     *
     * SETTINGS
     *
     * ######################################################################
     */
    $vendor = 'Vendor';
    $extKey = 'my_ext';
    $moduleExtensionName = $vendor . '.' . $extKey;
    $mainModuleName = 'myextmain';

    \TYPO3\CMS\Core\Utility\ExtensionManagementUtility::addModule(
        $mainModuleName,
        '',
        '',
        '',
        [
            'name' => $mainModuleName,
            'access' => 'user,group',
            'iconIdentifier' => 'vendor-search',
            'labels' => [
                'll_ref' => 'LLL:EXT:my_ext/Resources/Private/Language/locallang_mod_myextmain.xlf',
            ],
        ]
    );
})();